13A.13 Case studies

13A.13.1The quant quake, August 2007#

Context By 2007 many hedge funds and proprietary desks ran quantitative equity market-neutral books: long and short baskets built from similar signals (value, momentum, short-term reversal), market-neutral and levered.

Timeline and evidence Khandani and Lo (2007; revised 2011) study the week of 6 August 2007, when several such funds suffered losses their managers described as unprecedented. Their tool is a simple contrarian strategy (after Lehmann 1990 and Lo and MacKinlay 1990) that buys the previous day's losers and sells the winners in proportion to their deviation from the equal-weighted market return, $w_{i,t} = -\tfrac1N(R_{i,t-1} - R_{m,t-1})$: a cross-sectional stat-arb portfolio betting that relative moves revert. In the 2007 paper, the losses of such funds and of the simulated strategy were concentrated in the week of 6 August, with a sharp rebound on 10 August. They hypothesise that one or more large quantitative market-neutral portfolios were rapidly unwound, probably a forced liquidation by a multi-strategy fund or proprietary desk that needed cash because of losses elsewhere (the summer of 2007 was the start of the credit crisis), and that the losses spread to similar portfolios through stop-loss and deleveraging rules. In the 2011 version, using factor portfolios and transactions data, they report that the unwind began in July 2007, with a brief episode on 1 August and a more sustained one from the open on 6 August, starting in financial-sector stocks and involving long book-to-market and short earnings-momentum positions; a simulated market-making strategy's returns were significantly negative during the week of 6 August and positive before and after, consistent with market makers withdrawing capital from 8 August. They argue that the disruption began outside the equity market and that systemic risk in the hedge-fund industry had increased.

Mechanism in this module's terms

• Each fund's spreads were plausibly mean-reverting in normal times. But mean reversion in a spread is not a law; it is the result of someone providing liquidity against temporary pressure. When the liquidity providers themselves were the ones selling, the spreads widened precisely because everyone held them.
• Crowding makes the P&L of "independent" spreads correlated across funds in a stress, so the diversification assumed in sizing disappears exactly when needed.
• The rebound on 10 August shows the spreads did revert. Those forced to cut at the worst point realised the loss; those with capital and nerve to hold did not. Under the OU model, the expected P&L of holding through an adverse move is positive; the binding constraint was funding, not expectation (Shleifer and Vishny 1997).

13A.13.2HDFC Bank and ICICI Bank: a pair that broke around a merger#

Context and dated facts

• 4 Apr 2022: the boards of HDFC Ltd (the mortgage lender) and HDFC Bank approved the merger of HDFC Ltd into HDFC Bank, at 42 HDFC Bank shares for every 25 HDFC shares. On the day HDFC closed up 9.3% at ₹2,678.90 and HDFC Bank up 9.97% at ₹1,656.45 (as reported by news aggregators; one report misdates the closing figures to 4 March). Our Yahoo series gives a 10.0% HDFC Bank close-to-close move that day, consistent with the report.
• 1 Jul 2023: the merger took effect. HDFC Ltd shares last traded on 12 Jul 2023 and were suspended from 13 Jul 2023, the record date for the swap; HDFC Ltd's F&O contracts were finally settled on 12 Jul 2023 (NSE circular as reported by Business Today). HDFC Bank allotted 3,11,03,96,492 new shares to HDFC shareholders (Outlook Business).

Two pairs, two fates

1. HDFC Ltd and HDFC Bank moved from level 4 to level 1 of the ladder in 13A.1 on 4 April 2022. From then on $\ln P^{\text{HDFC}} - \ln P^{\text{HDFCB}} - \ln(42/25)$ was tied to zero at completion by contract, and its value before completion was a merger-arbitrage spread: at the reported closes of 4 Apr 2022, $\tfrac{42}{25}\times1{,}656.45 = \text{₹}2{,}782.84$ against ₹2,678.90, a 3.88% gross spread to be earned over an uncertain completion period (Problem 13A.18). Pricing that spread as a probability-weighted payoff is the subject of M06A. A statistical model fitted to the pre-announcement relationship was irrelevant after the announcement.
2. HDFC Bank and ICICI Bank were never convincingly cointegrated (13A.12.1), but the "same sector, similar franchise" story led many to treat them as a pair. From the announcement close (4 Apr 2022) to 4 Nov 2026, adjusted for dividends and corporate actions, HDFC Bank's price relative was 0.95 and ICICI Bank's 1.98. From the effective date (3 Jul 2023, first trading day after) the relatives were 0.90 and 1.56. The OLS hedge ratio in levels fell from 1.13 (2015–19) to 0.38 (2020–26). Yet, as 13A.10.5 showed, the return beta and correlation were essentially unchanged across the merger date.

Mechanism A pairs trader who bought HDFC Bank and sold ICICI Bank each time the spread "widened by two standard deviations" after mid-2023 would have been adding to a loser repeatedly: the spread trended. Market commentary at the time attributed HDFC Bank's relative performance to the effect of absorbing a large mortgage book funded largely by borrowings on its deposit and margin metrics; we have not verified that attribution and do not rely on it. The statistical lesson does not depend on the cause: (i) return correlation, which did not break, is not evidence of a level tie; (ii) a merger that changes one leg's balance sheet is a pre-specified break date, after which the relationship must be re-established from new data, not assumed; (iii) the Engle–Granger evidence was weak even before the event, so there was never a statistical case for the trade.